Astrophysical jets are observed as stable structures, extending in lengths several times their radii. The role of various instabilities and how they affect the observed jet properties has not been fully understood. Using the ideal relativistic MHD equations to describe jet dynamics we aim to study the stability properties through linear analysis.
In this work we probe stability properties of jets without current sheets and low magnetizations, moving with mildly relativistic Lorentz factors. In particular we find the dispersion relation for kink $ (m = \pm 1) $ and pinch $(m=0)$ modes. In the former we find that a wide range of wavelengths $ \sim $ 1 - 1000 jet radii equally contributes to the instability with growth rates $\sim $ a few $10^{-3}c/r_j$, while in the latter the large wavelengths are more unstable, giving similar growth rates. Evaluating the eigenfunctions of the instability we see that they attain their highest values near the jet boundary, indicating that the instabilities are most likely of a Kelvin-Helmholtz type rather than current driven.